Afterward, we generate a transition matrix \(A\)  by computing the embedding similarity of each pair of instances at different time frames, where each element \(A_{t}^{t+1}(i,j)\)  stands for the transition probability of the \(i^{th}\)  instance at time \(t\)  to the \(j^{th}\)  instance at time \(t+1\) .
By using the idea of cycle consistency loss [1]}, [2]}, [3]}, if the \(i^{th}\)  instance at time \(t\)  is able to transit (similar) to the \(j^{th}\)  instance at time \(t+1\) , the inverse transition should also hold.
Thus, we encourage the diagonal elements in the multiplication results of these two transition matrices \(A_{t}^{t+1}\)  and \(A_{t+1}^{t}\)  to have large values by comparing them with an identity matrix (\(I\) ):
\(L^{cyc} \ = \ C_{en}(A_{t}^{t+1}A_{t+1}^{t},I) \ .\) 
